ITERATIVE POSITIVE SOLUTIONS FOR SINGULAR RIEMANN-STIELTJES INTEGRAL BOUNDARY VALUE PROBLEM

By applying iterative technique, we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that $f(t,u)$ is non-increasing respect to $u$.     

TRIPLE POSITIVE SOLUTIONS TO A CLASS OF m-POINT BOUNDARY VALUE PROBLEM OF SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATION

By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green's functions of the problems are also given.     

POSITIVE SOLUTIONS OF FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS

1IntroductionInthispaper,weconsidertheexistenceofpositivesolutionsoftheequationwithoneofthefollowingsetsofboundaryvalueconditionsWhenthefunctionf(x,y)p)inequation(l.1)isoftheformf(x,y,p)Hy,theboundaryvalueproblem(l.1)-(1.2)describesthedeformationsofanelasticbeambothofwhoseendssimplysupportedat0and1,andtheboundaryvalueproblem(1.l)-(l.3)describesanelasticbeamwithoneofitsendsimplysupportedandtheotherendclampedbyslidingclamps.In[11,Aftabizadehshowedtheexistenceofasolutionto(l.l)-(l.2)undertherest…     

POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.     

POSITIVE SOLUTION TO SECOND-ORDER FOUR-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY

This paper considers the positive solution to a class of second-order four-point boundary value problem, in which the first order derivative is involved in the nonlinear term explicitly. By the fixed point theorem in cone, sufficient conditions ensuring the existence of positive solution to the problem are obtained. An example is given to illustrate the feasibility of the main results.     

TRIPLE SYMMETRIC POSITIVE SOLUTIONS TO NONLINEAR BVP WITH INTEGRAL BOUNDARY VALUE CONDITIONS

In the paper,we consider a nonlinear boundary value problem with integral boundary value conditions.By a generalization of the Leggett-Williams fixed-point theorem,we provide sufficient conditions for the existence of at least three positive solutions to the problem.An example is introduced to demonstrate our result.     

EXISTENCE OF AT LEAST THREE POSITIVE SOLUTIONS TO MULTI-POINT BOUNDARY VALUE PROBLEM WITH p-LAPLACIAN OPERATOR

In this paper,we consider a multi-point boundary value problem. We obtain suffcient conditions ensuring the existence of at least three positive solutions to the boundary value problem.     

高耦合边值问题正解的存在性

本文通过研究非线性项f(t,x1,x2…，xn-1）和g(t,y1,y2…yn-1)的性质，给出了高阶耦合边值问题至少存在一个正解的条件，同时，运用该结论建立了两个正解的存在性定理。     

TRIPLE POSITIVE SOLUTIONS FOR A CLASS OF SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM

By using fixed-point theorems, some new results for multiplicity of positive solutions for a class of second order m-point boundary value problem are obtained. The associated Green's function of this problem is also given.     

MULTIPLE POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

This paper is concerned with the existence of positive solutions to singular boundary value problems of functional differential equations with p-Laplacian. Under the suitable conditions,the existence of three positive solutions is esta- blished by using an abstract fixed point theorem.     

MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.     

POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,we establish sufficient conditions for the existence of positive solutions to a general class of integral boundary value problem(BVP) of nonlinear fractional functional differential equation.A differential operator is taken in the RiemannLiouville sense.Our analysis relies on the Krasnosel'skii fixed-point theorem in cones.We also give examples to illustrate the applicability of our results.     

一类四阶奇异边值问题对称正解的最优存在性

本文研究了一类四阶奇异边值问题.通过建立一个特定的锥,利用Leggett-Williams不动点定理,从而在一定的条件下得到一类四阶奇异边值问题对称正解的最优存在性,推广了奇异边值问题对称正解的最优存在性的结果.     

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u‘‘‘ ρ^3u = f(t,u), 0 ≤ t ≤ 2π, with u^(i)(0) = u^(i)(2π), i = 0,1,2, where ρ ∈ (0, 1 /√3) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2π] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.     

POSITIVE SOLUTIONS OF HIGHER DIMENSIONAL DISCRETE BOUNDARY VALUE PROBLEM

By means of the critical point theory, we prove the existence of positive solutions for a higher dimensional discrete boundary value problem. Our results generalize one of Agarwal in [2].     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

POSITIVE SOLUTIONS TO A NONHOMO- GENEOUS NONAUTONOMOUS SECOND- ORDER BOUNDARY VALUE PROBLEM

The existence of multiple positive solutions is studied for a nonlinear nonauto- nomous second-order boundary value problem with nonhomogeneous boundary con- ditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel＇skii fixed point theorems on a cone, several new results are proved.     

MULTIPLE POSITIVE SOLUTIONS OF A SINGULAR (n-1,1) CONJUGATE BOUNDARY VALUE PROBLEM WITH DELAY

§ 1　IntroductionThe study of boundary value problems(abbr.as BVP) for ordinary differential equa-tions has a long history and there are many papers and wonderful results about it(for ex-ample,refer to [1～ 5] and the references therein) .Recently,[3 ] discussed the existenceproblem of at least one positive solution for some(n-1 ,1 ) conjugate boundary value prob-lem as follows:u(n) (t) a(t) f(u) =0 ,(0 相似文献   

POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

By constructing a special cone and using the fixed point theorem of cone expansion and compression,this paper investigates fourth-order singular boun- dary value problems with sublinear effect and presents some necessary and sufficient conditions for existence of C~2 or C~3 positive solutions.Further,some examples are given concerning the applications of our main results.     

EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM

In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.